Cementitious composite constituent relationships

A cementitious composite, comprising:

• a first layer;
• a second layer spaced from the first layer;
• and
• a cementitious mixture disposed between the first layer and the second layer, the cementitious mixture including cementitious materials and non-cementitious materials, wherein the cementitious mixture at least one of (i) includes colloidal cement, (ii) is compacted in a specific arrangement, and (iii) undergoes a specific treatment process to provide particles with a certain shape and size, and wherein the cementitious mixture has a bulk volume including (i) a volume of the cementitious materials of the cementitious mixture, (ii) a volume of the non-cementitious materials of the cementitious mixture, and (iii) a volume of the voids within the cementitious mixture;
• wherein the cementitious materials are shaped and arranged such that prior to the in-situ hydration:
• V
• b
• =
• M
• c
• ρ
• c
• 
• (
• 1
• +
• F
• v
• )
• +
• ∑
• i
• n
• 
• M
• nc
• i
• ρ
• nc
• i
• where:
• Vb is the bulk volume of the cementitious mixture per unit area of the cementitious composite;
• Mc is a mass of the cementitious materials of the cementitious mixture per unit area of the cementitious composite;
• ρc is a density of the cementitious materials of the cementitious mixture;
• Mnci is a mass of each constituent type of the non-cementitious materials of the cementitious mixture per unit area of the cementitious composite;
• βnci is a density of each constituent type of the non-cementitious materials of the cementitious mixture;
• and
• Fv is a ratio of the volume of the voids within the cementitious mixture relative to the volume of the cementitious materials of the cementitious mixture per unit area of the cementitious composite, wherein Fv is between 0.10 and 5;
• and
• wherein the cementitious mixture is configured to absorb a mass of water that provides a maximum 28 day compressive strength of the cementitious composite;
• and
• wherein:
• Mw=x·Mc
• where:
• Mw is the mass of the water per unit area of the cementitious composite;
• Mc is a mass of the cementitious materials of the cementitious mixture per unit area of the cementitious composite;
• and
• x is a ratio of the mass of the water relative to the mass of the cementitious materials of the cementitious mixture per unit area of the cementitious composite that provides the maximum 28 day compressive strength of the cementitious composite, wherein x is between 0.25 and 0.55.

A cementitious composite, comprising:

• a first layer;
• a second layer spaced from the first layer;
• and
• a cementitious mixture including cementitious materials disposed between the first layer and the second layer, and wherein the cementitious mixture has a bulk volume including (i) a volume of the cementitious materials of the cementitious mixture and (ii) a volume of the voids within the cementitious mixture;
• wherein the cementitious materials are shaped and arranged such that prior to the in-situ hydration:
• V
• b
• =
• M
• c
• ρ
• c
• 
• (
• 1
• +
• F
• v
• )
• where:
• Vb is the bulk volume of the cementitious mixture per unit area of the cementitious composite;
• Mc is a mass of the cementitious materials of the cementitious mixture per unit area of the cementitious composite;
• ρc is a density of the cementitious materials of the cementitious mixture;
• and
• Fv is a ratio of the volume of the voids within the cementitious mixture relative to the volume of the cementitious materials of the cementitious mixture per unit area of the cementitious composite, wherein Fv is between 0.30 and 0.64 such that the cementitious composite is configured for high pressure hydration applications.